Is there a problem using the secular names for the days of the week?
If there is a problem, is it because:
1) The names originally come from Polytheistic gods
2) The people forbidding them are doing so because they believe we should distance ourselves from anything secular.
I know in addition to the Hebrew names, there are Yiddish names I have seen used.
From One of Rabbi Edley's articles:
In the Mechilta (Shemot 20; 8) (The commandment stating to "Remember the day of Shabbat") it states: Rabbi Yitzchak says, ‘Don’t count like the others count, rather you should count for Shabbat’. The explanation is that non-Jews count the days of the week with names, each day has its own name, either names of heavenly bodies [or gods] (Sunday, Monday etc.) like the Christians do, or other names. However Israel count each day with reference to Shabbat, ‘First day from Shabbat’, ‘Second day from Shabbat’ etc.. This is part of the Mitzvah that we are commanded to remember Shabbat every day. This is the simple meaning of the verse and is also the explanation of Ibn Ezra.
It is unclear from this explanation if this is a halacha, per se, or if this is a statement of what Jews do by habit, or otherwise.
However, see This article which quotes the stringency of the Chassam Sofer, and claims that this was (is still?) the Hungarian custom. According to Chasam Sofer (Toras Moshe, Parashas Bo), there is an obligation to begin one’s letters with the number of the day of the week (counting from Sunday), and the number of the month (counting from Nissan): “This is an explicit rebuke [to those who do not use the Jewish calendar]: We should write in our letters and similar documents the first day of the week, first month of the year, and so on, to testify that Hashem created the world in six days, ‘and He rested on the seventh,’ and to remember the redemption from Egypt—and not Heaven forbid, the date of the nations.”
I recommend reading the whole article as it also lists contemporary opinions. The ruling by Rav Ovadia Yosef permits using secular dates (he explains month names, not day names, though).
Although the names of the months and angels were brought up from Bavel, as is brought in the yerushalmi, rosh hashanah 1 2, and pointed to in tosafos rosh hashana 7a, the point i haven't seen mentioned but seems very important is that the olei gola returned to Eretz Yisroel from Persia, the conquerors of Babylon. The Persians used a solar calendar and most definitely did not worship the same gods as the Babylonians, so at the time the anshei kinesses hagdola were using the Babylonian months, that is in megilas Esther and in Daniel, they were referring to worthless has been gods. In fact the name adar which comes from aduru was the name of the Assyrian chief deity and it is supposed thats why the leap month was attributed to him, a seeming inferior position. So we are dealing with a former god twice removed from his position of authority. And so even though Mordechai got his name from marduk and Esther got her name from ishtar, we can assume they no longer held religious prominence.
If we can use this as a klal gadol, than former has beens would be okay to use. It is also the svara Rabbi Belsky told me when I asked him why no one minds wearing Nike sneakers, nike being the god of victory in war. He said noone knows or cares about that god anymore.
Because of the OP's concern, the Pri Megadim actually writes that one should not use the Yiddish names for the days of the week, but this ruling does not seem to be followed. In truth, as other answers mentioned, it is not such a problem because nobody worships those gods anymore.
Moreover, according to the Satmar Rebbe and Rabbi Menachem Kasher, the commandment to start counting the week from Shabbos only means that once a day a person should mention how many days have passed since Shabbos. Because we already do this in the liturgical introduction to the Shir Shel Yom, we need not follow that directive the rest of the day and can use other terms/names for the days of the week.
SOURCE: "Uttering the Names of Idols" by Reuven Cham Klein printed in the Journal of Halacha and Contemporary Society vol. 73, pgs. 5-21.
